The question was not written properly above.
Complete Question :
Lea's car travels an average of 30 miles per gallon of gas. If she spent $20.70 on gas for 172.5 mile trip, what was the approximate cost of gas in dollars per gallon?
Answer:
$3.6
Step-by-step explanation:
From the above question, we have the following information:
For
30 miles = 1 gallon of gas
We are also told she travelled,
$20.70 on gas for 172.5 miles
Step 1
Find how many gallons of gas was issued in the 172.5 miles
30 miles = 1 gallon of gas
172.5 miles = y
Cross multiply
30 × y = 172.5 miles × 1
y = 172.5 miles/30
y = 5.75 gallons
Therefore, for 172.5 miles she used 5.75 gallons of gas
Step 2
For step 2 we find the approximate cost of gas in dollars per gallon
$20.70 = 172.5 miles = 5.75 gallons of gas
Hence,
5.75 gallons of gas = $20.70
1 gallon of gas = $X
Cross Multiply
5.75 gallons × $X = $20.70 × 1 gallon
$X = $20.70 × 1 gallon/ 5.75 gallons
$X = $3.6
X = $3.6
Therefore, the approximate cost of gas in dollars per gallon = $3.6
Given:g(x)= x-4 and h(x)= 2x-8 What are the restrictions on the domain of g•h? x>
Answer:
[tex] g(x) =\sqrt{x-4}[/tex]
[tex] h(x) =2x-8[/tex]
And we want to find:
[tex] g o h(x)[/tex]
Replacing we got:
[tex] go h(x)= \sqrt{2x-8 -4}= \sqrt{2x-12}[/tex]
And the restriction for this case would be:
[tex] 2x-12 \geq 0[/tex]
[tex] 2x \geq 12[/tex]
[tex] x \geq 6[/tex]
Step-by-step explanation:
Assumign that we have the following two functions:
[tex] g(x) =\sqrt{x-4}[/tex]
[tex] h(x) =2x-8[/tex]
And we want to find:
[tex] g o h(x)[/tex]
Replacing we got:
[tex] go h(x)= \sqrt{2x-8 -4}= \sqrt{2x-12}[/tex]
And the restriction for this case would be:
[tex] 2x-12 \geq 0[/tex]
[tex] 2x \geq 12[/tex]
[tex] x \geq 6[/tex]
Chapter 8 Written Homework 1. A hypothesis test is conducted to test the claim that the proportion of people with dark hair at Moorpark is greater than 0.8. The researchers find that the test statistic is z = 2.19. a. Using ???? = 0.05, draw a bell-shaped curve to represent the critical value approach. Be sure to label (This means find and label the critical value as well as the rejection and fail to reject regions). b. Based on your drawing would we reject of fail to reject? Explain.
Answer:
we reject H₀
Step-by-step explanation: Se annex
The test is one tail-test (greater than)
Using α = 0,05 (critical value ) from z- table we get
z(c) = 1,64
And Test hypothesis is:
H₀ Null hypothesis μ = μ₀
Hₐ Alternate hypothesis μ > μ₀
Which we need to compare with z(s) = 2,19 (from problem statement)
The annex shows z(c), z(s), rejection and acceptance regions, and as we can see z(s) > z(c) and it is in the rejection region
So base on our drawing we will reject H₀
Trigonometry.....Help plzzzz
Answer:
17.3 = AC
Step-by-step explanation:
Since this is a right angle, we can use trig functions
tan B = opp/ adj
Tan 68 = AC / 7
7 tan 68 = AC
17.32560797 = AC
To 1 decimal place
17.3 = AC
Answer:
AC = 17. 3 cmStep-by-step explanation:
To find AC we use tan
tan ∅ = opposite / adjacent
From the question
AB is the adjacent
AC is the opposite
So we have
tan 68 = AC / AB
AC = AB tan 68
AC = 7 tan 68
AC = 17.32
AC = 17. 3 cm to one decimal place
Hope this helps you
The graph shows the growth of a tree with
representing the number of years since it was allanted
and y representing the trees het mees Use the
graph to analyze the trees growth. Sellest alltaf sly
The tree was 40 metes taill when planted
The tree's growth rate is 10 mees per year
The tree was 2 years old when planted
As it ages, the trees growth rate shows
Ten years after planting, is 14 inches tall
Answer:
The tree was 40 inches tall when planted
The tree's growth rate is 10 inches per year
Ten years after planting, is 140 inches tall
Step-by-step explanation:
From the graph attached, the height of the tree is plotted on the y axis and the year is on the x axis. The line passes through (2, 60) and (5, 90). The equation of a line passing through two point is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Therefore the equation of the line passing through (2, 60) and (5, 90) is:
[tex]y-60=\frac{90-60}{5-2}(x-2) \\y-60=\frac{30}{3} (x-2)\\y-60=10(x-2)\\y-60=10x-20\\y=10x-20+60\\y=10x+40[/tex]
The equation of a line in standard form is y = mx + c where c is the intercept on y axis and m is the slope. Since y = 10x + 40, m = 10 and c = 40.
The y intercept is 40 inches, this means the height of the tree at 0 years was 40 inches tall when planted, therefore The tree was 40 inches tall when planted is correct.
The slope of the line is 10, this means the tree grow at a rate of 10 inches per year. Therefore The tree's growth rate is 10 inches per year is correct.
The tree was 2 years old when planted is not correct
The slope of a linear function is constant, therefore the growth rate is constant. As it ages, the trees growth rate slows is not correct
The height of the tree at 10 years can be gotten by substituting x = 10 in y = 10x + 40. y = 10(10) + 40 = 100 + 40 = 140 inches. Therefore Ten years after planting, it is 140 inches tall. is correct
Simplify (1.92.2.4%)?(1.93.2.42):3
Answer:
1/16.4616
Step-by-step explanation:
(1.9^2*2.4^-3) (1.9^3*2.4^-2)^-3
(1.9^2*2.4^-3) * 1 / (1.9^3*2.4^-2)^3
1.9^2*2.4^-3 / (1.9^3*2.4^-2)^3
1.9^2 * 1 / 2.4^3 ÷ (1.9^3* 1 / 2.4^2)3
1.9^2 / 2.4^3 × (2.4^2/1.9^3)^3
(1/2.4) (1/1.9)^3
(1/2.4) (1/6.859)
1/16.4616
Un avión volaba a 14.800 metros de altura. Primero bajó 23.000 decímetros y luego bajó 54 Hectómetros más ¿ A qué altura, en Kilómetros, vuela ahora? AYUDA
Answer:
7.1 km
Step-by-step explanation:
Bien, este es un problema de conversión de unidades.
Procedemos de la siguiente manera;
Convirtamos todas las alturas que tenemos a metros.
Comenzamos con 23,000 decímetros a metros Matemáticamente, 1 metro = 10 decímetros Entonces 23,000 decímetros = 23,000 / 10 = 2,300 metros
En segundo lugar, convertimos 54 hectómetros a metros.
Matemáticamente; 1 hectómetro = 100 metros Entonces 54 hectómetros = 54 * 100 = 5400 metros Por lo tanto, su nueva altura sería; 14,800-2300-5400 = 7,100 metros Ahora, procedemos a convertir 7.100 metros a kilómetros.
Matemáticamente 1000 m = 1 km Entonces 7,100 m serán = 7100/1000 = 7.1 km
Responder:
7,1 kilómetrosExplicación paso a paso:
Altura inicial del avión = 14.800 m.
Como se redujo en 23,000 decímetros y luego en 54 hectómetros, la caída total de altura se obtiene al agregar 23,000 decímetros y 54 hectómetros
Antes de agregarlos, necesitamos convertir ambos valores a metros
1 decímetro = 0.1m
23,000 decímetros = x
x = 23,000 * 0.1
x = 2,300 metros
Además, si 1 hectómetro = 100 m
54 hectómetros = y
y = 54 * 100
y = 5400 metros.
Sumando ambas alturas;
x + y = 2300m + 5400m = 7700 metros
Esto significa que el avión cae por una altura total de 7700 metros
Para calcular la altura a la que volará el avión después de la caída, tomaremos la diferencia entre la altura inicial y la altura total caída.
La altura que el avión está volando ahora será 14,800 - 7,700 = 7,100 metros
Convirtiendo la respuesta final a kilómetros.
1000m = 1km
7.100m = z
z = 7100/1000
z = 7.1 km
Esto significa que el avión está volando a una altura de 7.1 kilómetros después de la caída.
Find the product : 2p (4p² + 5p + 7)
Explanation:
The outer term 2p is distributed among the three terms inside the parenthesis. We will multiply 2p by each term inside
2p times 4p^2 = 2*4*p*p^2 = 8p^3
2p times 5p = 2*5*p*p = 10p^2
2p times 7 = 2*7p = 14p
The results 8p^3, 10p^2 and 14p are added up to get the final answer shown above. We do not have any like terms to combine, so we leave it as is.
What is the decibel level of the sound of a ticking clock with intensity 10−9 watts per square inch? Use a logarithmic model to solve.
Answer:
β = (-0.19 dB).
Step-by-step explanation:
The formula which is used to calculate the decibel level of a sound is given by :
[tex]\beta=10\log (\dfrac{I}{I_o})[/tex]
I is intensity of the sound of a ticking clock
[tex]I_o=10^{-12}\[/tex] watts per square meter
Since, [tex]1\ \text{inch}^2=\dfrac{1}{1550}\ \text{m}^2[/tex]
The intensity of a monster truck is converted into per square meter as follows:
[tex]10^{-9}\ {W/in^2}= \dfrac{10^{-9}}{1550}\ W/m^2\\\\10^{-9}\ {W/in^2}=6.45\times 10^{-13}\ W/m^2[/tex]
So, Decibal level is :
[tex]\beta=10\log (\dfrac{6.45\times 10^{-13}}{10^{-12}})\\\\\beta =-0.19\ dB[/tex]
So, the decibel level of the sound of a ticking clock is (-0.19 dB).
Answer:
30dB
Step-by-step explanation:
A film distribution manager calculates that 9% of the films released are flops.If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%? Round your answer to four decimal places.
Answer:
the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% is 0.0042
Step-by-step explanation:
Given that :
A film distribution manager calculates that 9% of the films released are flops
Let p be the probability for the movies that were released are flops;
[tex]\mu_p = P = 0.9[/tex]
If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%
now; we know that our sample size = 442
the standard deviation of the variance is [tex]\sigma_p= \sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.9(1-0.9)}{442}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.9(0.1)}{442}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.09}{442}}[/tex]
[tex]\sigma_p= \sqrt{2.0361991 \times 10^{-4}}[/tex]
[tex]\sigma _p = 0.014[/tex]
So; if the manager is right; the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% can be calculated as:
[tex]P(|p-P|>0.04)=1 -P(p-P|<0.04)[/tex]
[tex]P(|p-P|>0.04)=1 -P(-0.04 \leq p-P \leq 0.04)[/tex]
[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{\sigma_p} \leq \dfrac{ p-P}{\sigma_p} \leq \dfrac{0.04}{\sigma_p})[/tex]
[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{0.014} \leq Z\leq \dfrac{0.04}{0.014})[/tex]
[tex]P(|p-P|>0.04)=1 -P( -2.8571 \leq Z\leq 2.8571)[/tex]
[tex]P(|p-P|>0.04)=1 -[P(Z \leq 2.8571) -P (Z\leq -2.8571)[/tex]
[tex]P(|p-P|>0.04)=1 -(0.9979 -0.0021)[/tex]
[tex]P(|p-P|>0.04)=1 -0.9958[/tex]
[tex]\mathbf{P(|p-P|>0.04)=0.0042}[/tex]
∴
the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% is 0.0042
What is m∠A? please help
Answer: 50 degrees
Step-by-step explanation:
180-85=95
180-145=35
interior angle sum for a triangle is 180 degrees, so 180=95+35+a
m of angle A is 50 degrees
Solve the inequality 47.75 + x Less-than-or-equal-to 50 to determine how much more weight can be added to Li’s suitcase without going over the 50-pound limit. What is the solution set?
x Less-than-or-equal-to 2.25
x Less-than-or-equal-to 2.75
x Greater-than-or-equal-to 2.25
x Greater-than-or-equal-to 2.75
Answer: x Less-than-or-equal-to 2.25
Step-by-step explanation:
The given inequality: 47.75 + x Less-than-or-equal-to 50.
To determine: How much more weight can be added to Li’s suitcase without going over the 50-pound limit.
i.e. inequality for x.
[tex]47.75+x\leq50[/tex]
Subtract 47.75 from both the sides, we get
[tex]x\leq50-47.75\\\\\Rightarrow\ x\leq2.25[/tex]
So, the solution set is "x Less-than-or-equal-to 2.25"
Hence, the correct answer is "x Less-than-or-equal-to 2.25."
Answer
A x <_ 2.25
Step-by-step explanation:
Look at the amount of soft drink in each bottle of capacity 2L, given here. How much more soft drink should be added to completely fill each of the bottles?
Answer:
1992.50 mL; 825 mL
Step-by-step explanation:
Given that :
Capacity of bottles in the attachment = 2L
Amount of soft drink in bottle 1 = 7.50mL
Amount of soft drink in bottle 2 = 1175mL
Converting liter milliliter
1Litre = 1000 milliliters
Therefore 2Litres = 2000 milliliters
Capacity each of bottle = 2000 milliliters
Volume of drink required to completely fill bottle 1:
2000mL - 7.50mL = 1992.50 mL
Volume of drink required to completely fill bottle 2:
2000mL - 1175mL = 825 mL
n unknown number y is 10 more than an unknown number x. The number y is also x less than 3. The equations to find x and y are shown below. y = x + 10 y = −x + 3 Which of the following statements is a correct step to find x and
Answer:
Add the equations to eliminate x.
Step-by-step explanation:
(1) y = 10 + x
(2) y = 3 - x
An easy way to solve this problem is to add the two equations to eliminate x.
(3) 2y = 13
From here, you can calculate y and then x.
Which equation represents a population of 300 animals that decreases at an annual rate of 23% ?
Answer:
n × 0.77
Step-by-step explanation:
Decreasing a number by 23% is the same as multiplying that number by 0.77, so n number of animals decreased by 23% is:
n × 0.77
What is the quotient?
Answer:
3/2
Step-by-step explanation:
● (-3/8) ÷(-1/4)
Flip the second fraction by putting 1 instead 4 and vice versa.
● (-3/8)* (-4/1)
-4 over 1 is -4 since dividing by 1 gives the same number.
● (-3/8)*(-4)
Eliminate the - signs in both fractions since multiplying two negative numbers by each other gives a positive number.
●( 3/8)*4
● (3*4/8)
8 is 2 times 4
● (3*4)/(4*2)
Simplify by eliminating 4 in the fraction.
● 3/2
The result is 3/2
ASAP!!! PLEASE help me with this question! I am really stuck...
Answer:
8π cm^2
Step-by-step explanation:
We proceed as follows;
To answer this question, what we need firstly is the name of the cross section that results from slicing a sphere into half.
The cross section that results is called a hemisphere, which is half the size of the sphere.
But before we can calculate the area of the new cross section, we will need the radius of the original shape.
This is obtainable from the volume of the shape.
Mathematically;
Volume of a sphere = 4/3 * π * r^3
32/3 * π = 4/3 * π * r^3
We can take off π/3 from both sides so we are left with;
32 = 4r^3
Divide through by 4
r^3 = 8
r is the cube root of 8 = 2 cm
Now we find the area of the hemisphere
Mathematically, the area of a hemisphere is 2 * π * r^2
using the value of r = 2 cm given above, we have Hemisphere area = 2 * π * 2^2 =8 π cm^2
4) Flying to Tahiti with a tailwind a plane averaged 259 km/h. On the return trip the plane only
averaged 211 km/h while flying back into the same wind. Find the speed of the wind and the
speed of the plane in still air.
A) Plane: 348 km/h, Wind: 37 km/h B) Plane: 243 km/h, Wind: 30 km/h
C) Plane: 235 km/h, Wind: 24 km/h D) Plane: 226 km/h, Wind: 13 km/h
fundraiser Customers can buy annle nies and
Answer: C) Plane: 235 km/h, Wind: 24 km/h
Step-by-step explanation:
Given that :
Average Speed while flying with a tailwind = 259km/hr
Return trip = 211km/hr
Let the speed of airplane = a, and wind speed = w
Therefore ;
Average Speed while flying with a tailwind = 259km/hr
a + w = 259 - - - (1)
Return trip = 211km/hr
a - w = 211 - - - (2)
From (2)
a = 211 + w
Substitute the value of a into (1)
a + w = 259
211 + w + w = 259
211 + 2w = 259
2w = 259 - 211
2w = 48
w = 48/2
w = 24km = windspeed
Substituting w = 24 into (2)
a - 24 = 211
a = 211 + 24
a = 235km = speed of airplane
WILL MARK BRAINLIEST!!! PLZ HELP!!!
Answer:
median
Step-by-step explanation:
(median is used to measure the middle)
you just line up all the numbers from least to greatest, then pick the middle number, IF there are NO numbers in the middle, you add the the 2 middle numbers up, then divided by 2
Answer:
Median, because there is 1 outlier that affects the center
Step-by-step explanation:
"The median is the middle number of the data set. It is exactly like it sounds. To figure out the median you put all the numbers in order (highest to lowest or lowest to highest) and then pick the middle number. If there is an odd number of data points, then you will have just one middle number."
(1) 4p²q : 10pq²
(2) 9 months : 2/½ years
(3) 5 m : 600 cm
I need answers asap, thanks!! <3
Answer: (1) 2p: 5q.
(2) 3:10.
(3) 5:6.
Step-by-step explanation:
To find : Ratio
(1) 4p²q : 10pq²
[tex]=\dfrac{4p^2q}{10pq^2}\\\\=\dfrac{2p^{2-1}}{5q^{2-1}}\\\\=\dfrac{2p}{5q}[/tex]
i.e. Simplified ratio of 4p²q : 10pq² is 2p: 5q.
(2) 9 months : 2½ years
1 year = 12 months
[tex]2\dfrac{1}{2}\text{years}=\dfrac{5}{2}\text{years}\\\\=\dfrac{5}{2}\times12=30\text{ months}[/tex]
Now, 9 months : 2½ years = [tex]\dfrac{9\text{ months}}{30\text{ months}}=\dfrac{3}{10}[/tex]
Hence, Simplified ratio of 9 months : 2½ years is 3:10.
(3) 5 m : 600 cm
1 m = 100 cm
So, 5m = 500 cm
Now, 5 m : 600 cm = [tex]\dfrac{500\ cm}{600\ cm}=\dfrac{5}{6}[/tex]
Hence, Simplified ratio of 5 m : 600 cm is 5:6.
A patient's temperature went down from 105.85 to 99.1 as a result of taking 5 mg. of a certain drug. What was the rate at which her temperature decreased per milligram?
Answer:
1.35 degrees per mg.
Step-by-step explanation:
The patient's temperature went from 105.85 to 99.1. That is a decrease of 6.75 degrees. You want to find the temperature decrease per milligram, which can be found by dividing the temperature by the number of mg of the drug.
6.75 / 5 = 675 / 500 = 1.35
So, the rate at which her temperature decreased per milligram is 1.35 degrees per mg.
Hope this helps!
Please help as soon as possible
Your question has been heard loud and clear.
Answer is option d or the fourth option.
thank you
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
second one
Step-by-step explanation:
The function g has this expression g(x) = ax²+c
to have a minimum a should be positive since the parabola will open upTo find when g reaches it's minimum we must derivate it
g(x) = ax²+cg'(x) = 2axsolve g'(x) = 0
g'(x) = 02ax = 0ax = 0x = 0replace x with 0 in g(x)
g(0) = a(0)²+c
g(0) = c
the maximum of f(x) is 1 so for g(x) to have a grather minimum c should be greather than 1
the second statement is true
f(x) = 4x^4 – 2x^3 – 3x^2 + 6x - 9 Find the Zeros Using Descartes' Rule of Signs
Answer:
So possibilities of zeroes are:
Positive Negative Imaginary
1 1 2
3 1 0
Zeroes = -1.4549, 1.2658, 0.34457-1.0503i, 0.34457+1.0503i.
Step-by-step explanation:
Note: Descartes' Rule of Signs is used to find the signs of zeroes not the exact value.
The given function is
[tex]f(x)=4x^4-2x^3-3x^2+6x-9[/tex]
Degree of polynomial is 4 so number of zeroes is 4.
There are three sign changes, so there are either 3 positive zeros or 1 positive zero.
Now, put x=-x in f(x).
[tex]f(-x)=4(-x)^4-2(-x)^3-3(-x)^2+6(-x)-9[/tex]
[tex]f(-x)=4x^4+2x^3-3x^2-6x-9[/tex]
There is one variation in sign change, so there is 1 negative zero.
So possibilities of zeroes are:
Positive Negative Imaginary
1 1 2
3 1 0
Using graphing calculator the zeroes of given function are -1.4549, 1.2658, 0.34457-1.0503i and 0.34457+1.0503i.
Find the focus. y= -1/12 (x)² - 6
Answer:
[tex]\Large \boxed{\sf\ \ (0,-9) \ \ }[/tex]
Step-by-step explanation:
Hello,
We know that when the parabola equation is
[tex]y=a(x-h)^2+k[/tex]
the vertex is (h,k) and the focus is
[tex](h,k+\dfrac{1}{4a})[/tex]
Here, the equation is
[tex]y=-\dfrac{1}{12}x^2-6[/tex]
so
[tex]a=-\dfrac{1}{12}\\\\h = 0\\\\k =-6[/tex]
So,
[tex]k+\dfrac{1}{4a}=-6-\dfrac{12}{4}=-6-3=-9[/tex]
Then, the focus is
[tex]\large \boxed{\sf\ \ (0,-9) \ \ }[/tex]
I attached the graph, included the focus so that you can see it :-)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The length of ZX is 2 units. What is the perimeter of triangle XYZ? 5 + + 2 units 5 + 3 units 5 + + 2 units 10 + 2 units
Answer:
B) 5 + 3√5 units
Step-by-step explanation:
The length of ZX is 2√5 units. What is the perimeter of triangle XYZ?
A) 5 +√3 + 2 √5 units
B) 5 + 3√5 units
C) 5 + √6 + 2√5 units
D) 10 + 2√5 units
From the diagram attached, point X is at (-1, 4), Y(3, 1), Z(1, 0).
The distance between two point
[tex]O(x_1,y_1)\ and\ A(x_2,y_2)\ is\ given\ as:\\\\OA=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The lengths of the sides of the triangle are:
[tex]|XY| = \sqrt{(3-(-1))^2+(1-4)^2}=\sqrt{25} =5\ unit\\ \\|XZ|= \sqrt{(1-(-1))^2+(0-4)^2}=\sqrt{20} =2\sqrt{5} \ unit\\\\|YZ|= \sqrt{(1-3)^2+(0-1)^2}=\sqrt{5} \ unit[/tex]
The perimeter of the triangle is the sum of all the sides, i.e.
Perimeter = |XY| + |YZ| + |XZ| = 5 + 2√5 + √5 = 5 + 3√5
Answer:
B
Step-by-step explanation:
Find f o g and g o f to determine if f and g are inverse functions. If they are not inverses, pick the function that would be the inverse with f(x). F(x) = -4x + 1; g(x) = (x+1)/4 Choices: a. G(x) has to be: (1-x)/4 b. Inverses c. G(x) has to be: 1/(4 - x) d. G(x) has to be: x/4
Answer:
G(x) = (1 - x)/4
is the inverse function required.
Step-by-step explanation:
Given F(x) = -4x + 1
Let y = F(x)
Then y = -4x + 1
=> y - 1 = -4x
4x = 1 - y
x = (1 - y)/4
That is, the inverse is (1 - x)/4
Therefore, G(x) has to be (1 - x)/4
need help ASAP thanks
Answer:
[tex]b = 74\ cm[/tex]
Step-by-step explanation:
The volume of a prism is given by the following equation:
[tex]Volume = base\ area * height[/tex]
In our case, the base is a triangle, so the area is given by:
[tex]base\ area = base * height_{\Delta}/2[/tex]
The base of the triangle is 43 cm, the height of the triangle is b, the height of the prism is 24 and the volume of the prism is 38,184, so we have:
[tex]base\ area = 43 * b/2 = 21.5b[/tex]
[tex]38184 = 21.5b * 24[/tex]
[tex]b = 38184/(24*21.5)[/tex]
[tex]b = 74\ cm[/tex]
1) (23-36-) + (1) + (8426
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HELLP PLEASE
Compute the integral with respect to x, then with respect to y:
[tex]\displaystyle16\int_0^\pi\int_0^1x^2\sin y\,\mathrm dx\,\mathrm dy=16\int_0^\pi\sin y\frac{x^3}3\bigg|_0^1\,\mathrm dy[/tex]
[tex]=\displaystyle\frac{16}3\int_0^\pi\sin y\,\mathrm dy[/tex]
[tex]=\displaystyle\frac{16}3(-\cos y)\bigg|_0^\pi=\boxed{\dfrac{32}3}[/tex]
Alternatively, in this case you can "factorize" the integral as
[tex]\displaystyle16\left(\int_0^\pi\sin y\,\mathrm dy\right)\left(\int_0^1x^2\,\mathrm dx\right)[/tex]
and get the same result.
What the correct answer now
Answer:
Area of the triangle WXY = 111.8 mm²
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinX}}{\text{WY}}=\frac{\text{SinY}}{\text{WX}}[/tex]
Since m∠W + m∠X + m∠Y = 180°
m∠W + 26° + 130° = 180°
m∠W = 180° - 156°
m∠W = 24°
[tex]\frac{\text{Sin24}}{\text{XY}}=\frac{\text{Sin130}}{31}=\frac{\text{Sin26}}{\text{WX}}[/tex]
[tex]\frac{\text{Sin24}}{\text{XY}}=\frac{\text{Sin130}}{31}[/tex]
XY = [tex]\frac{31\times (\text{Sin24})}{\text{Sin130}}[/tex]
XY = 16.4597
≈ 16.4597 mm
Area of the triangle = [tex]\frac{1}{2}(\text{XY})(\text{WY})\text{SinY}[/tex]
= [tex]\frac{1}{2}(16.4597)(31)\text{Sin26}[/tex]
= 111.83 mm²
≈ 111.8 mm²
Therefore, area of the triangle WXY = 111.8 mm²
JM is the perpendicular bisected of LM. Which segments are congruent?
A. JN and LN
B. JN and NM
C. LN and NK
D. NK and NM
Answer:
LN and NK
Step-by-step explanation:
trust
Answer: c
Step-by-step explanation:
Its correct